$A$ ball of mass $m$ moving with a velocity of $9 \ m/s$ collides with another ball of the same mass $m$ at rest. After the collision,both balls move at an angle of $30^\circ$ with the original direction of motion. Find the velocity $v$ of both balls after the collision. (in $m/s$)

$A$ particle of mass $m$ moving with speed $2v$ collides with a mass $2m$ moving with speed $v$ in the same direction. After the collision,the first mass is stopped completely,while the second one splits into two particles each of mass $m$,which move at an angle of $45^o$ with respect to the original direction. The speed of each of the moving particles will be:

$A$ particle falls from a height $h$ upon a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution,the total distance travelled before rebounding has stopped is

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2m$ at rest. If the coefficient of restitution is $0.4$,the ratio of the velocities of the spheres $A$ and $B$ after collision is

$A$ small steel ball bounces on a steel plate held horizontally. On each bounce,the speed of the ball arriving at the plate is reduced by a factor $e$ (coefficient of restitution) in the rebound,so that $V_{\text{upward}} = e V_{\text{downward}}$. If the ball is initially dropped from a height of $0.4 \text{ m}$ above the plate and if $10 \text{ s}$ later the bouncing ceases,the value of $e$ is:

$A$ particle of mass $m_1$ moving along the $X$-axis collides with a stationary particle of mass $m_2$ and deviates by an angle $30^{\circ}$ to the $X$-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by $50 \%$,then the ratio of the masses $\frac{m_2}{m_1}$ is